Fractal Branching Organizations of Ediacaran Rangeomorph Fronds Reveal a Lost Proterozoic Body Plan

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Fractal Branching Organizations of Ediacaran Rangeomorph Fronds Reveal a Lost Proterozoic Body Plan Fractal branching organizations of Ediacaran rangeomorph fronds reveal a lost Proterozoic body plan Jennifer F. Hoyal Cuthill1 and Simon Conway Morris Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, United Kingdom Edited by Andrew H. Knoll, Harvard University, Cambridge, MA, and approved June 17, 2014 (received for review May 8, 2014) The branching morphology of Ediacaran rangeomorph fronds has morphology than was previously possible. These parameters are no exact counterpart in other complex macroorganisms. As such, then used to reconstruct 3D space-filling strategies within the these fossils pose major questions as to growth patterns, func- group and evaluate potential frond functions, revealing an tional morphology, modes of feeding, and adaptive optimality. adaptive radiation of fractal organizations. This provides a new Here, using parametric Lindenmayer systems, a formal model of framework for the study of growth, functional morphology, rangeomorph morphologies reveals a fractal body plan character- and evolution of these lost constructions. ized by self-similar, axial, apical, alternate branching. Consequent morphological reconstruction for 11 taxa demonstrates an adap- Results and Discussion tive radiation based on 3D space-filling strategies. The fractal body Our L-system model comprises an initial axiom (starting plan of rangeomorphs is shown to maximize surface area, consis- branch segment), production rules for axial, apical, and alternate tent with diffusive nutrient uptake from the water column (osmo- branching; and 28 parameters which together control branch trophy). The enigmas of rangeomorph morphology, evolution, and production, elongation rates, and 3D branching angles (SI Ap- extinction are resolved by the realization that they were adaptively pendix, Table S1). This incorporates both (sub) apical branch optimized for unique ecological and geochemical conditions in the production (distal extremities form the sites for subsequent late Proterozoic. Changes in ocean conditions associated with the branching) and expansion (branches grow in length and diameter Cambrian explosion sealed their fate. throughout life), based on relative branch sizes and potential ontogenetic series (4, 6, 7, 20, 21). At each step in the axial paleobiology | paleontology branching process, an apical branch segment (e.g., the tip of the stem) produces one lateral branch segment (e.g., the beginning n parallel with large-scale geochemical transitions associated of a new primary lateral branch) and an additional axis segment – – Iwith ocean oxygenation (1 3), the Ediacaran Period (635 541 (e.g., the new stem apex) (Fig. 1, SI Appendix, and Movies S1– Ma) records a major diversification of multicellular eukaryotes. S3). Lateral branches are produced alternately (e.g., left then – Rangeomorph fronds (575 541 Ma) dominated early Ediacaran right) along a branch axis. Reconstruction of overall morpholo- biotas (4) and have a characteristic branching morphology, dis- gies that closely match the anatomy of the fossils (Fig. 2 and tinct from any known Phanerozoic organism (5). Although the SI Appendix) validates this model of branching and growth. fronds are often preserved as flattened impressions, exceptional Collectively, these reconstructions demonstrate how different moldic fossils preserve details of the 3D branching structure to body shapes and symmetry patterns [characteristics relied upon a resolution of 30 μm (6). Qualitative classifications for rangeo- morph branching patterns have been proposed (7, 8), but no Significance quantitative model has previously been formulated. Because branching is repeated over decreasing size scales (with up to four Rangeomorph fronds characterize the late Ediacaran Period observed orders of branching), rangeomorph fronds have been – informally described as self-similar and fractal (4–6). Although (575 541 Ma), representing some of the earliest large organ- this has potential implications for the functional optimality of their isms. As such, they offer key insights into the early evolution of multicellular eukaryotes. However, their extraordinary branch- morphologies (5, 9), the extent to which they are formally fractal ing morphology differs from all other organisms and has proved and self-similar (10, 11) has not previously been tested. Further- highly enigmatic. Here we provide a unified mathematical model more, until now, evolutionary transitions in branching patterns of rangeomorph branching, allowing us to reconstruct 3D have not been characterized within any quantitative framework. morphologies of 11 taxa and measure their functional proper- Rangeomorphs inhabited shallow to abyssal marine environ- – ties. This reveals an adaptive radiation of fractal morphologies ments (1, 8, 12 14), evidently precluding photosynthesis for most which maximized body surface area, consistent with diffusive taxa (12). Preservational features, including bending and over- nutrient uptake (osmotrophy). Rangeomorphs were adap- folding (4, 15), suggest that rangeomorphs were soft-bodied. No tively optimal for the low-competition, high-nutrient con- evidence exists for either motility or active feeding (such as ditions of Ediacaran oceans. With the Cambrian explosion in musculature, filter feeding organs, or a mouth). Consequently, animal diversity (from 541 Ma), fundamental changes in eco- rangeomorphs have been reconstructed as sessile, feeding on logical and geochemical conditions led to their extinction. organic carbon by diffusion (or possibly endocytosis) through the body surface (3, 5, 12, 16), with a large surface area to volume Author contributions: J.F.H.C. designed research; J.F.H.C. performed research; J.F.H.C. ratio aiding nutrient uptake (5, 16). The adaptive potential analyzed data; and J.F.H.C. and S.C.M. wrote the paper. of their different branching morphologies has, however, never The authors declare no conflict of interest. been quantified. This article is a PNAS Direct Submission. Here, using parametric Lindenmayer systems (L-systems) (17, See Commentary on page 12962. 18), we present a unified model to describe the branching 1To whom correspondence should be addressed. Email: [email protected]. structure of Ediacaran rangeomorph fronds. Our quantitative This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. parameters provide a far more detailed definition of frond 1073/pnas.1408542111/-/DCSupplemental. 13122–13126 | PNAS | September 9, 2014 | vol. 111 | no. 36 www.pnas.org/cgi/doi/10.1073/pnas.1408542111 Downloaded by guest on September 28, 2021 due to alternate branching on the right and left of an axis (7)], bilateral or tetraradial symmetry in apical view, and helical tor- SEE COMMENTARY sion around the main body axis (Fig. 3 and SI Appendix). Previous descriptions (following ref. 6) informally suggested that rangeomorphs possessed a shared fractal module consisting of a centimeter-scale, self-similar frondlet (conceptually similar to the primary lateral branch and associated subbranches, as formalized here). We demonstrate that rangeomorph morphologies can be re- constructed by applying approximately self-similar branch pro- duction rules (as described above) at increasingly fine scales, although these may be modified by different parameter values to give subtle variations in the level of self-similarity (SI Appendix,TableS1). These production rules apply across the branching system of the frond [sometimes called the petalodium (8)], from the stem (the 0-order branch, which produces the first-order lateral branches) to the highest order of branching (that is, from the third-order branches) (Fig. 1). This reveals that self-similarity extends beyond the frondlet, previously hypothesized to represent the basic modular unit (6). That is to say, the entire rangeomorph frond shows approximately self- similar branching, whereas the basic unit repeated throughout the frond is a cylindrical branch segment. This branch segment can be broadly related (6) to Seilacher’s concept of the fractal pneu (24). We also show that rangeomorph fronds are approximately fractal (10) with noninteger fractal dimensions of 1.6–2.4 as determined Fig. 1. Schematic L-system model of Beothukis mistakensis.(A) First three steps of the branching process. (B) Final morphology at step 38. Segment colors in- by the 3D box counting method (SI Appendix,Fig.S13). dicate relative age, from oldest (red) to youngest (light blue). Numbers indicate Shared possession of an approximately self-similar and fractal, branch order (0, stem; 1, primary; 2, secondary; 3, tertiary; and 4, quaternary). axial, apical, and alternate branching body plan supports a ran- geomorph clade (Rangeomorpha, Pflug, 1972, cited in ref. 8) but significantly increases the range of diagnostic characters [pre- by some previous comparative studies (22, 23)] emerge from viously restricted to repeated fine-scale branching (8) only visible variations on a shared branching pattern. Resulting body or- in exceptionally preserved specimens]. Note that this rangeo- ganizations include alternate-symmetry (also known as glide- morph body plan does not extend to other enigmatic Ediacaran symmetry) in frontal view [superficially bilateral symmetry, offset macroorganisms, such as Swartpuntia, Ernietta (8), or Dickinsonia EVOLUTION Fig. 2. Ediacaran rangeomorph fossils and their 3D L-system models. (A and B) Avalofractus abaculus. A reproduced with permission from ref. 4, figure 3.1. (C and D) Charnia masoni.(C) South
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